Riemannian Geometry: A Modern Introduction / Edition 2

by Isaac Chavel

Overview

Requiring only an understanding of differentiable manifolds, Isaac Chavel covers introductory ideas followed by a selection of more specialized topics in this second edition. He provides a clearer treatment of many topics, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. Among the classical topics shown in a new setting is isoperimetric inequalities in curved spaces. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.

Product Details

ISBN-13:	9780521619547
Publisher:	Cambridge University Press
Publication date:	04/10/2006
Series:	Cambridge Studies in Advanced Mathematics , #98
Edition description:	REV
Pages:	488
Product dimensions:	5.98(w) x 9.02(h) x 0.98(d)

About the Author

Isaac Chavel is Professor of Mathematics at The City College of the City University of New York. He received his Ph.D. in Mathematics from Yeshiva University under the direction of Professor Harry E. Rauch. He has published in international journals in the areas of differential geometry and partial differential equations, especially the Laplace and heat operators on Riemannian manifolds. His other books include Eigenvalues in Riemannian Geometry (1984) and Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives (Cambridge University Press, 2001). He has been teaching at The City College of the City University of New York since 1970, and has been a member of the doctoral program of the City University of New York since 1976. He is a member of the American Mathematical Society.

Table of Contents

1. Riemannian manifolds; 2. Riemannian curvature; 3. Riemannian volume; 4. Riemannian coverings; 5. Surfaces; 6. Isoperimetric inequalities (constant curvature); 7. The kinetic density; 8. Isoperimetric inequalities (variable curvature); 9. Comparison and finiteness theorems.

Editorial Reviews

"Each chapter concludes with an excellent section of notes and advanced exercises with further results, with hints and sketches of solutions at the end of the book...I think that it is the best reference on Riemannian geometry available, especially for someone interested in isoperimetric problems...Chavel is one of about a dozen mathematics books I keep at home for ready reference."
Frank Morgan, SIAM Review

From the Publisher